Abstract: A high damping condition is easily obtained in Mn-(16~24)Cu-(4~6)Ni-2Fe (at. pct) alloys,when cooling rate is controlled after the solid solution treatment at 1173 K. It is observed that the temperature dependent changes of Iogarithmic decrement in 10 h cooled samples are sensitive to the alloy composition. As compared with water quenching treatment, controlled 10 h cooling improves TN temperature of the alloys extensively by producing a Mn-enriched matrix portion in the alloys. Calcuiations suggest that the relative decreases of Cu and Ni content in the matrix portion be dominated by the Ni content in the original alloys, and therefore, the volume fraction of the Cu, Ni-enriched precipitates is estimated to be about 20% and 10% in the 4Ni and 6Ni alloys, respectively. As a result, the TN temperature fOr each alloy, corresponding to the rising temperature of logarithmic decrement, has been related to the Cu, and Ni content in the Mnenriched matrix. The existence of {110} twinning boundaries is confirmed in the microstructure of both 4Ni and 6Ni alloys. However, the relative lattice strains, which the twinning boundaries act to accommodate, are found largely different in the two alloys. It is considered that boundaries with smaller orientation deviation could coordinate the external Stresses easily by cyclic moving, and therefore, the broader damping peak which occurs in the 10 h cooled 6Ni alloy becomes feasible. Electron diffraction results also indicate possible for mation of many sub-crystals in the matrix phase, which are relatively rotated on some invariant planes. Those sub-crystal boundaries might play some attenuation roles in the temperature range between TN and room temperature.